Efficient Hop ID based Routing for Sparse Ad Hoc Networks

Yao Zhao1, Bo Li2, Qian Zhang2,

Yan Chen1, Wenwu Zhu31 Lab for Internet & Security Technology, Northwestern University

2 Hong Kong University of Science and Technology

3 Microsoft Research Asia

Outline

• Motivation

• Hop ID and Distance Function

• Dealing with Dead Ends

• Evaluation

• Conclusion

Dead End Problem

• Geographic distance dg fails to reflect hop distance dh (shortest path length)

E DS

A

),(),( DEdDAd hh

),(),( DAdDEd gg

But

Fabian Kun, Roger Wattenhofer and Aaron Zollinger, Mobihoc 2003

GFG/GPSR

GOAFR+

bett

erw

orse

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Network Density [nodes per unit disk]

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critical

Greedy success

Connectivity

Geographic routing suffers from dead end problem in sparse networks

Motivation

Related Work to Dead End Problem

• Fix dead end problem– Improves face routing: GPSR, GOAFR+, GPVF

R– Much longer routing path than shortest path

• Reduce dead ends“Geographic routing without location inform

ation” [Rao et al, mobicom03] – Works well in dense networks– Outperforms geographic coordinates if obstacle

s or voids exist– Virtual coordinates are promising in reducing de

ad ends– However, degrades fast as network becomes sp

arser

• Motivation

• Hop ID and Distance Function

• Dealing with Dead Ends

• Evaluation

• Conclusion

Outline

Virtual Coordinates

• Problem definition– Define and build the virtual

coordinates, and– Define the distance function based

on the virtual coordinates– Goal: routing based on the virtual

coordinates has few dead ends even in critical sparse networks • virtual distance reflects real distance• dv ≈ c · dh , c is a constant

What’s Hop ID

• Hop distances of a node to all the landmarks are combined into a vector, i.e. the node’s Hop ID.

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L1

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L3650

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A

Lower and Upper Bounds

• Hop ID of A is• Hop ID of B is

),,,( )1()1(2

)1(1 mHHH

),,,( )2()2(2

)2(1 mHHH

),(),(),( BAdLBdLAd hihih

),(|),(),(| BAdLBdLAd hihih

UHHMindHHMaxL kkk

hkkk

)(|)(| )2()1()2()1(

A

B

Li

• Triangulation inequality

(1)

(2)

How Tight Are The Bounds?

• Theorem [FOCS'04)]– Given a certain number (m) of

landmarks, with high probability, for most nodes pairs, L and U can give a tight bound of hop distance • m doesn’t depend on N, number of

nodes

– Example: If there are m landmarks, with high probability, for 90% of node pairs, we have U≤1.1L

Lower Bound Better Than Upper Bound

• One example: 3200 nodes, density λ=3π• Lower bound is much closer to hop distance

LU

0

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Lower bound vs Upper bound

L

U

Difference to Hop Distance

0 1 23 4 >4

650

Lower Bound Still Not The Best

• H(S) = 2 1 5• H(A) = 2 2 4• H(D) = 5 4 3• L(S, D) = L(A, D) = 3• |H(S) – H(D)|= 3 3 2• |H(A) – H(D)|= 3 2 1 22

4215

036

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L1

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L2

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4

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L3

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S DA

Other Distance Functions

• Make use of the whole Hop ID vector

• If p = ∞,

• If p = 1,

• If p = 2,

• What values of p should be used?

p

m

k

pkkp HHD

1

)2()1( ||

m

kkkp HHD

1

)2()1( ||

m

kkkp HHD

1

2)2()1( ||

LDp

The Practical Distance Function

• The distance function d should be able to reflect the hop distance dh

– d ≈ c · dh , c is a constant– L is quite close to dh (c = 1)

• If p = 1 or 2, Dp deviates from L severely and arbitrarily

• When p is large, Dp ≈ L ≈ dh

– p = 10, as we choose in simulations

Power Distance Better Than Lower Bound

LDp

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gePower distance vs Lower bound

L

Dp

Difference to Hop Distance

[0,1) [1,2) [2,3)[3, 4) [4,5) ≥5

• 3200 nodes, density λ=3π

Outline

• Motivation

• Hop ID and Distance Function

• Dealing with Dead Ends

• Evaluation

• Conclusion

Dealing with Dead End Problem

• With accurate distance function based on Hop ID, dead ends are less, but still exist

• Landmark-guided algorithm to mitigate dead end problem– Send packet to the closest landmark to

the destination– Limit the hops in this detour mode

• Expending ring as the last solution

Example of Landmark Guided Algorithm

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L2416

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S

DDp(L2, D)>Dp(S,D)Dead End

P

Detour

Mode

Greedy

Mode

A

Dp(S, D)>Dp(A, D)

Practical Issues

• Landmark selection– O(m·N) where m is the number of landm

arks and N is the number of nodes

• Hop ID adjustment– Mobile scenarios– Integrate Hop ID adjustment process int

o HELLO message (no extra overhead)

• Location server– Can work with existing LSes such as CA

RD, or– Landmarks act as location servers

Outline

• Motivation

• Hop ID and Distance Function

• Dealing with Dead Ends

• Evaluation

• Conclusion

Evaluation Methodology

• Simulation model– Ns2, not scalable– A scalable packet level simulator

• No MAC details• Scale to 51,200 nodes

• Baseline experiment design– N nodes distribute randomly in a 2D square– Unit disk model: identical transmission range

• Evaluation metrics– Routing success ratio– Shortest path stretch– Flooding range

Evaluation Scenarios

• Landmark sensitivity• Density• Scalability• Mobility• Losses• Obstacles• 3-D space• Irregular shape and voids

Simulated Protocols

• HIR-G: Greedy only• HIR-D: Greedy + Detour• HIR-E: Greedy + Detour + Expending ring• GFR: Greedy geographic routing • GWL: Geographic routing without location

information [Mobicom03]• GOAFR+: Greedy Other Adaptive Face

Routing [Mobihoc03]

0

0.25

0.5

0.75

1

2 10 18 26 34 42 50

Number of Landmarks

Ro

utin

g S

ucc

ess

Ra

tio

HIR-G λ=3πHIR-D λ=3πHIR-G λ=2πHIR-D λ=2π

Number of Landmarks• 3200 nodes, density shows average number of

neighbors• Performance improves slowly after certain value

(20)• Select 30 landmarks in simulations

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Number of Landmarks

Flo

od

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ng

e

λ=3πλ=2π

Density

• HIR-D keeps high routing success ratio even in the scenarios with critical sparse density.

• Shortest path stretch of HIR-G & HIR-D is close to 1.

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Network Density

HIR-GHIR-DHIR-EGFRGOAFR+GWL

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of S

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st P

ath

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Network Density

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ss R

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HIR-DHIR-GGFRGWL

Scalability

• HIR-D degrades slowly as network becomes larger• HIR-D is not sensitive to number of landmarks

Conclusions

• Hop ID distance accurately reflects the hop distance and

• Hop ID base routing performs very well in sparse networks and solves the dead end problem

• Overhead of building and maintaining Hop ID coordinates is low

Thank You!

Questions?

Lower Bound vs Upper Bound

• Lower bound is much close to hop distance

LU

0

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0.4

0.5

Pe

rce

nta

geLower bound vs Upper bound

L

U

Difference to Hop Distance

0 1 23 4 >4

• If two nodes are very close and no landmarks are close to these two nodes or the shortest path between the two nodes, U is prone to be an inaccurate estimation

• U(A, B) = 5, while dh(A, B)=2

U Is Not Suitable for Routing

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A

B

Landmark Selection

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Hop ID Adjustment

• Mobility changes topology

• Reflooding costs too much overhead

• Adopt the idea of distance vector

03

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30

21 2

3

24

13 Neighbor

s{23, 13}

Neighbors

{23}

Build Hop ID System

• Build a shortest path tree• Aggregate landmark candidates• Inform landmarks• Build Hop ID

– Landmarks flood to the whole network.

• Overall cost– O(m*n), m = number of LMs, n=numbe

r of nodes

Mobility

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0 300 600 900 1200 1500 1800

Pause time(s)

Suc

cess

Rat

io

HIR-G(λ=3π)HIR-D(λ=3π)HIR-G(λ=5π)HIR-D(λ=5π)

GFG/GPSR

GOAFR+

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Network Density [nodes per unit disk]

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• Geographic routing suffers from dead end problem in sparse networks• Fabian Kun, Roger Wattenhofer and Aaron Zollinger, Mobihoc 2003

Motivation

bett

erw

orse

1

2

3

4

5

6

7

8

9

Sh

ort

est

Pa

th S

pa

n

Greedy success

Connectivity

critical

Virtual Coordinates

• Problem definition– Define the virtual coordinates

• Select landmarks• Nodes measure the distance to landmarks• Nodes obtain virtual coordinates

– Define the distance function– Goal: virtual distance reflects real

distance

– dv ≈ c · dh , c is a constant